I heard a theorem in differential geometry course.
State of the theorem is
"There is no closed (regular) surface having only negative Gaussian curvature."
I tried to prove the theorem using Gauss-Bonnet theorem, but coudn't have any progress.
How can I get proof?
+) I guess that above theorem is also true when the word 'negative Gaussian curvature' is replaced with 'nonpositive Gaussian curvature'. Is this right?